Anomalous exchange interaction between intrinsic spins in conducting graphene systems

We address the nature and possible observable consequences of singular one-electron states that appear when strong defects are introduced in the metallic family of graphene, namely, metallic carbon nanotubes and nanotori. In its simplest form, after creating two defects on the same sublattice, a state may emerge at the Fermi energy presenting very unusual properties: It is unique, normalizable, and features a wave function equally distributed around both defects. As a result, the exchange coupling between the magnetic moments generated by the two defects is anomalous. The intrinsic spins couple ferromagnetically, as expected, but do not present an antiferromagnetic excited state at any distance. We propose the use of metallic carbon nanotubes as an electronic device based on this anomalous coupling between spins which can be useful for the robust transmission of magnetic information at large distances.

Figure 1

Schematic views of a metallic nanotorus (upper figure) and of our proposed experimental setup based on a metallic nanotube with two defects and a scanning tunneling microscopy tip.

Figure 2

(a) Electronic spectrum close to zero energy in a CNT(6,6) nanotorus with 9 unit cells. (b) Wave functions for one defect. (c) The same for two defects that generate a bilocal state. The shaded panel shows this state.

Figure 3

Magnetic moments per atom for ferro- (black) and antiferromagnetic (red) states of an AA pair in a metallic nanotorus (top) and semiconducting one (bottom). In the metallic case there is no antiferromagnetic state. The insets show the low-energy spectrum in the four cases, including the nonmagnetic one (blue).

Figure 4

DOS (top panel) and conductance (bottom panel) of a CNT(6,6) with different defects configurations as explained in the legend. The dashed lines correspond to second-nearest-neighbor hopping for one case.

Figure 5

DOS at zero energy projected on all atoms for a CNT(6,6) (unrolled view) with two defects positioned at a distance of 2.15 nm (a) and 5.2 nm (b) from each other. The inset shows the decay of the maximum LDOS around the defects as a function of the relative distance.